Originally Posted by Fabrik8

That's probably not the problem. The problem is that the ballast radiates electrical noise like an antenna. It's got a (switchmode) power supply in it that takes the battery voltage, switches it at some high frequency with FETs into a square wave, and steps the voltage up through a transformer. That's how the high voltage for the HIDs is created. The problem is that the transformer acts like an antenna, the FETs give off wideband EMF, and the whole process introduces switching noise on the power and ground wires.
A metal case for the ballasts can't stop EMF over the whole frequency range that is produced, so some can get coupled into the radio as either EMF or ground noise.

I can't say what exactly is causing the noise, but I'm going to assume that part of it is a poor quality radio receiver, part of it is probably a poor ground to the radio, and part of it is a poor quality power supply section in the radio.

This is really something that has to be dealt with through experimentation. Try changing where the ground on the radio is, make it as short as possible, and you could try isolating the ballasts with an insulating material (like double sided tape). It's a hard thing to troubleshoot without knowing what type of noise is actually causing the problem.